This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A049290 #26 Jun 05 2015 09:22:17
%S A049290 1,1,1,1,3,1,1,7,13,1,1,15,97,71,1,1,31,625,2143,461,1,1,63,3841,
%T A049290 54335,68641,3447,1,1,127,23233,1321471,8563601,3011263,29093,1,1,255,
%U A049290 139777,31817471,1035045121,2228419359,173773153,273343,1,1,511,839425
%N A049290 Array T(n,k) = number of subgroups of index k in free group of rank n, read by antidiagonals.
%D A049290 P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 23.
%D A049290 J. H. Kwak and J. Lee, Enumeration of graph coverings, surface branched coverings and related group theory, in Combinatorial and Computational Mathematics (Pohang, 2000), ed. S. Hong et al., World Scientific, Singapore 2001, pp. 97-161.
%D A049290 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(b).
%H A049290 Alois P. Heinz, <a href="/A049290/b049290.txt">Antidiagonals n = 1..37, flattened</a>
%H A049290 J. H. Kwak and J. Lee, <a href="http://com2mac.postech.ac.kr/resorce/Lecture_text.htm">Enumeration of graph coverings and surface branched coverings</a>, Lecture Note Series 1 (2001), Com^2MaC-KOSEF, Korea. See chapter 3. [Broken link?]
%H A049290 V. A. Liskovets and A. Mednykh, <a href="http://dx.doi.org/10.1080/00927870008826924">Enumeration of subgroups in the fundamental groups of orientable circle bundles over surfaces</a>, Commun. in Algebra, 28, No. 4 (2000), 1717-1738.
%e A049290 Array T(n,k) (n >= 1, k >= 1) begins:
%e A049290 1, 1, 1, 1, 1, ...
%e A049290 1, 3, 13, 71, 461, ...
%e A049290 1, 7, 97, 2143, 68641, ...
%e A049290 1, 15, 625, 54335, 8563601, ...
%p A049290 T:= proc(n,k) option remember; k* k!^(n-1) -add(j!^(n-1) *T(n, k-j), j=1..k-1) end: seq(seq(T(d+1-k, k), k=1..d), d=1..10); # _Alois P. Heinz_, Oct 29 2009
%t A049290 nmax = 10; t[n_, k_] := t[n, k] = k*k!^(n-1) - Sum[j!^(n-1)*t[n, k-j], {j, 1, k-1}]; Flatten[ Table[ t[n-k+1, k], {n, 1, nmax}, {k, 1, n}]] (* _Jean-François Alcover_, Nov 09 2011, after Maple *)
%Y A049290 Rows give A003319, A027837, A049291.
%Y A049290 Columns give A000225, A049294, A049295.
%Y A049290 Main diagonal is A057014.
%K A049290 nonn,easy,nice,tabl
%O A049290 1,5
%A A049290 _N. J. A. Sloane_, Sep 09 2000
%E A049290 More terms from _Alois P. Heinz_, Oct 29 2009